I've just been putting protective oil on a wooden door using a cloth and was getting the oil onto the cloth using the technique of blocking the tin with the cloth and upending the tin so that a small amount of oil is left on the cloth.

I've used this technique all my life for various things but have never known a word or phrase to describe the action. I also use it when cleaning things with white-spirit or similar. When I had a toothache as a child, my mother used to apply Oil of Cloves to the tooth from her finger-tip using a similar action.

If no-one has anything - let's make one up!